We develop a systematic theory of microwave-induced oscillations in magnetoresistivity of a 2D electron gas in the vicinity of fractional harmonics of the cyclotron resonance, observed in recent experiments. We show that in the limit of well-separated Landau levels the effect is dominated by the multiphoton inelastic mechanism. At moderate magnetic field, two single-photon mechanisms become important. One of them is due to resonant series of multiple single-photon transitions, while the other originates from microwave-induced sidebands in the density of states of disorder-broadened Landau levels.
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